Question

3;x;5;y form a quadratic number pattern
If the 2nd difference is 2, determine the value of x and y

Answer 1

Answer:

x = 3

y = 9

Step-by-step explanation:

To determine the values of x and y in the given quadratic number pattern, begin by finding the first differences. To do this, subtract each term from the next term:

$(x - 3)$

$(5 - x)$

$(y - 5)$

To find the second differences, subtract each first difference from the next first difference:

$(5-x)-(x-3)$

$(y-5)-(5-x)$

Given that the second difference is 2, we can set the two expressions for the second differences equal to 2, and solve for x and y.

$\begin{aligned}(5-x)-(x-3)&=2\\5-x-x+3&=2\\8-2x&=2\\-2x&=-6\\x&=3\end{aligned}$

$\begin{aligned}(y-5)-(5-x)&=2\\(y-5)-(5-3)&=2\;\;\;\leftarrow\textsf{Substitute x=3 }\\(y-5)-(2)&=2\\y-5-2&=2\\y-7&=2\\y&=9\end{aligned}$

Therefore, the values of x and y are:

$\huge\boxed{\boxed{\begin{aligned}x &= 3\\y& = 9\end{aligned}}}$